Physics-based data augmentation for the POD reduced-basis formulation of incompressible Navier-Stokes equations
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A posteriori reduced-order models based on Proper Orthogonal Decomposition (POD) are a well-established methodology for efficiently solving parametric problems. These methods require representative training sets of full-order solutions (snapshots) that capture all possible features in the parametric family of solutions. However, the computational cost of generating extensive training sets is often unaffordable. In this context, we propose a physics-based data augmentation strategy to enrich poorly populated training sets for the parametric incompressible Navier-Stokes equations. Artificial snapshots are generated by combining existing solutions while enforcing mass and momentum conservation principles. These new snapshots are generated at a fraction of the cost of full-order solutions and incorporate features that are not present in the original training set. The enriched training set leads to reduced basis approximations that better capture the physics of the flow. The approach is validated on two- and three-dimensional flow problems, showing superior performance in terms of accuracy and efficiency compared to standard reduced-order approximations.